Drying chilies is very easy. Usually, as long as they
are kept in a reasonably dry area (like a basement of an
air-conditioned home) they can be allowed to air dry. It
sometimes helps prevent mold growth if the chilies are
soaked in a mild bleach solution (1 tsp household bleach
per quart of tap water) for about 5 minutes before
hanging them to dry. An oven or home dehydrator will dry
the chilies much faster and more reliably but perfectly
satisfactory results can be obtained without expensive
equipment.

Source: Douglas Holt, Ph.D., Chair of
Food Science Program & State Extension Specialist for
Food Safety, University of Missouri-Columbia